Using the ETAS Model for Catalog Declustering and Seismic Background Assessment

Earthquake catalogs exhibit strong spatio-temporal correlations. As such, earthquakes are often classified into clusters of correlated activity. Clusters themselves are traditionally classified in two different kinds: (i) bursts, with a clear hierarchical structure between a single strong mainshock, preceded by a few foreshocks and followed by a power-law decaying aftershock sequence, and (ii) swarms, exhibiting a non-trivial activity rate that cannot be reduced to such a simple hierarchy between events.&#160;The Epidemic Aftershock Sequence (ETAS) model is a linear Hawkes point process able to reproduce earthquake clusters from empirical statistical laws [Ogata, 1998]. Although not always explicit, the ETAS model is often interpreted as the outcome of a background activity driven by external forces and a Galton-Watson branching process with one-to-one causal links between events [Saichev et al., 2005]. Declustering techniques based on field observations [Baiesi & Paczuski, 2004] can be used to infer the most likely causal links between events in a cluster. Following this method, Zaliapin and Ben&#8208;Zion (2013) determined the statistical properties of earthquake clusters characterizing bursts and swarms, finding a relationship between the predominant cluster-class and the heat flow in seismic regions.Here, I show how the statistical properties of clusters are related to the fundamental statistics of the underlying seismogenic process, modeled in two point-process paradigms [Bar&#243;, 2020].The classification of clusters into bursts and swarms appears naturally in the standard ETAS model with homogeneous rates and are determined by the average branching ratio (nb) and the ratio between exponents &#945; and b characterizing the production of aftershocks and the distribution of magnitudes, respectively. The scale-free ETAS model, equivalent to the BASS model [Turcotte, et al., 2007], and usual in cold active tectonic regions, is imposed by &#945;=b and reproduces bursts. In contrast, by imposing &#945;<0.5b, we recover the properties of swarms, characteristic of regions with high heat flow.&#160;Alternatively, the same declustering methodology applied to a non-homogeneous Poisson process with a non-factorizable intensity, i.e. in absence of causal links, recovers swarms with &#945;=0, i.e. a Poisson Galton-Watson process, with similar statistical properties to the ETAS model in the regime &#945;<0.5b.Therefore, while bursts are likely to represent actual causal links between events, swarms can either denote causal links with low &#945;/b ratio or variations of the background rate caused by exogenous processes introducing local and transient stress changes. Furthermore, the redundancy in the statistical laws can be used to test the hypotheses posed by the ETAS model as a memory&#8208;less branching process.&#160;References:<ul><li> Baiesi, M., & Paczuski, M. (2004). Physical Review E, 69, 66,106. doi:10.1103/PhysRevE.69.066106. </li> <li> Bar&#243;, J. (2020).&#160; Journal of Geophysical Research: Solid Earth, 125, e2019JB018530. doi:10.1029/2019JB018530. </li> <li> Ogata, Y. (1998) Annals of the Institute of Statistical Mathematics, 50(2), 379&#8211;402. doi:10.1023/A:1003403601725. </li> <li> Saichev, A., Helmstetter, A. & Sornette, D. (2005) Pure appl. geophys. 162, 1113&#8211;1134. doi:10.1007/s00024-004-2663-6. </li> <li> Turcotte, D. L., Holliday, J. R., and Rundle, J. B. (2007), Geophys. Res. Lett., 34, L12303, doi:10.1029/2007GL029696. </li> <li> Zaliapin, I., and Ben&#8208;Zion, Y. (2013), J. Geophys. Res. Solid Earth, 118, 2865&#8211; 2877, doi:10.1002/jgrb.50178. </li> </ul>

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Operational Earthquake Forecasting during the 2019 Ridgecrest, California, Earthquake Sequence with the UCERF3-ETAS Model

Seismological Research Letters ◽

10.1785/0220190294 ◽

2020 ◽

Vol 91 (3) ◽

pp. 1567-1578 ◽

Cited By ~ 3

Author(s):

Kevin R. Milner ◽

Edward H. Field ◽

William H. Savran ◽

Morgan T. Page ◽

Thomas H. Jordan

Keyword(s):

High Performance ◽

Aftershock Sequence ◽

Lessons Learned ◽

Ease Of Use ◽

Earthquake Forecasting ◽

Earthquake Rupture ◽

Etas Model ◽

Epidemic Type Aftershock Sequence ◽

Aftershock Sequences ◽

High Performance Computing Cluster

Abstract The first Uniform California Earthquake Rupture Forecast, Version 3–epidemic-type aftershock sequence (UCERF3-ETAS) aftershock simulations were running on a high-performance computing cluster within 33 min of the 4 July 2019 M 6.4 Searles Valley earthquake. UCERF3-ETAS, an extension of the third Uniform California Earthquake Rupture Forecast (UCERF3), is the first comprehensive, fault-based, epidemic-type aftershock sequence (ETAS) model. It produces ensembles of synthetic aftershock sequences both on and off explicitly modeled UCERF3 faults to answer a key question repeatedly asked during the Ridgecrest sequence: What are the chances that the earthquake that just occurred will turn out to be the foreshock of an even bigger event? As the sequence unfolded—including one such larger event, the 5 July 2019 M 7.1 Ridgecrest earthquake almost 34 hr later—we updated the model with observed aftershocks, finite-rupture estimates, sequence-specific parameters, and alternative UCERF3-ETAS variants. Although configuring and running UCERF3-ETAS at the time of the earthquake was not fully automated, considerable effort had been focused in 2018 on improving model documentation and ease of use with a public GitHub repository, command line tools, and flexible configuration files. These efforts allowed us to quickly respond and efficiently configure new simulations as the sequence evolved. Here, we discuss lessons learned during the Ridgecrest sequence, including sensitivities of fault triggering probabilities to poorly constrained finite-rupture estimates and model assumptions, as well as implications for UCERF3-ETAS operationalization.

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Integration of geological and seismological data in earthquakes occurrence models for Italy: towards a unified model for different forecast perspectives

Geophysical Journal International ◽

10.1093/gji/ggz419 ◽

2019 ◽

Vol 219 (3) ◽

pp. 2148-2164

Author(s):

A M Lombardi

Keyword(s):

Aftershock Sequence ◽

Earthquake Forecasting ◽

Short Term ◽

Background Rate ◽

Etas Model ◽

Term Forecast ◽

Earthquake Predictability ◽

Background Seismicity ◽

Different Types

SUMMARY The operational earthquake forecasting (OEF) is a procedure aimed at informing communities on how seismic hazard changes with time. This can help them live with seismicity and mitigate risk of destructive earthquakes. A successful short-term prediction scheme is not yet produced, but the search for it should not be abandoned. This requires more research on seismogenetic processes and, specifically, inclusion of any information about earthquakes in models, to improve forecast of future events, at any spatio-temporal-magnitude scale. The short- and long-term forecast perspectives of earthquake occurrence followed, up to now, separate paths, involving different data and peculiar models. But actually they are not so different and have common features, being parts of the same physical process. Research on earthquake predictability can help to search for a common path in different forecast perspectives. This study aims to improve the modelling of long-term features of seismicity inside the epidemic type aftershock sequence (ETAS) model, largely used for short-term forecast and OEF procedures. Specifically, a more comprehensive estimation of background seismicity rate inside the ETAS model is attempted, by merging different types of data (seismological instrumental, historical, geological), such that information on faults and on long-term seismicity integrates instrumental data, on which the ETAS models are generally set up. The main finding is that long-term historical seismicity and geological fault data improve the pseudo-prospective forecasts of independent seismicity. The study is divided in three parts. The first consists in models formulation and parameter estimation on recent seismicity of Italy. Specifically, two versions of ETAS model are compared: a ‘standard’, previously published, formulation, only based on instrumental seismicity, and a new version, integrating different types of data for background seismicity estimation. Secondly, a pseudo-prospective test is performed on independent seismicity, both to test the reliability of formulated models and to compare them, in order to identify the best version. Finally, a prospective forecast is made, to point out differences and similarities in predicting future seismicity between two models. This study must be considered in the context of its limitations; anyway, it proves, beyond argument, the usefulness of a more sophisticated estimation of background rate, inside short-term modelling of earthquakes.

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Testing of the foreshock hypothesis within an epidemic like description of seismicity

Geophysical Journal International ◽

10.1093/gji/ggaa611 ◽

2020 ◽

Author(s):

G Petrillo ◽

E Lippiello

Keyword(s):

Seismic Activity ◽

Good Description ◽

Aftershock Sequence ◽

Short Term ◽

Etas Model ◽

Temporal Clustering ◽

Epidemic Type Aftershock Sequence ◽

Preparatory Phase ◽

Spatio Temporal ◽

The One

Summary The Epidemic Type Aftershock Sequence (ETAS) model provides a good description of the post-seismic spatio-temporal clustering of seismicity and is also able to capture some features of the increase of seismic activity caused by foreshocks. Recent results, however, have shown that the number of foreshocks observed in instrumental catalogs is significantly much larger than the one predicted by the ETAS model. Here we show that it is possible to keep an epidemic description of post-seismic activity and, at the same time, to incorporate pre-seismic temporal clustering, related to foreshocks. Taking also into-account the short-term incompleteness of instrumental catalogs, we present a model which achieves very good description of the southern California seismicity both on the aftershock and on the foreshock side. Our results indicate that the existence of a preparatory phase anticipating mainshocks represents the most plausible explanation for the occurrence of foreshocks.

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Retrieval of reflections from seismic background-noise measurements

Geophysical Research Letters ◽

10.1029/2006gl028735 ◽

2007 ◽

Vol 34 (4) ◽

Cited By ~ 139

Author(s):

Deyan Draganov ◽

Kees Wapenaar ◽

Wim Mulder ◽

Johannes Singer ◽

Arie Verdel

Keyword(s):

Background Noise ◽

Noise Measurements ◽

Seismic Background

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How ETAS Can Leverage Completeness of Modern Seismic Networks Without Renouncing Historical Data

10.5194/egusphere-egu2020-5827 ◽

2020 ◽

Author(s):

Leila Mizrahi ◽

Shyam Nandan ◽

Stefan Wiemer

Keyword(s):

Reference Model ◽

Information Gain ◽

Quality Data ◽

Training Period ◽

Alternative Formulation ◽

Probabilistic Seismic Hazard Assessment ◽

Magnitude Of Completeness ◽

Gradual Improvement ◽

Etas Model ◽

Completeness Magnitude

The Epidemic-Type Aftershock Sequence (ETAS) model is often used to describe the spatio-temporal distribution of earthquakes. A fundamental requirement for parameter estimation of the ETAS model is the completeness of the catalog above a magnitude threshold mc. mc is known to vary with time for reasons such as gradual improvement of the seismic network, short term aftershock incompleteness and so on. For simplicity, nearly all applications of the ETAS model assume a global magnitude of completeness for the entirety of the training period. However, in order to be complete for the entire training period, the modeller is often forced to use very conservative estimates of mc, as a result completely ignoring abundant and high-quality data from the recent periods, which falls below the assumed mc. Alternatively, to benefit from the abundance of smaller magnitude earthquakes from the recent period in model training, the duration of the training period is often restricted. However, parameters estimated in this way may be dominated by one or two sequences and may not represent long term behavior.We developed an alternative formulation of ETAS parameter inversion using expectation maximization, which accounts for a temporally variable magnitude of completeness. To test the adequacy of such a technique, we evaluate its forecasting power on an ETAS-simulated synthetic catalog, compared to the constant completeness magnitude ETAS base model. The synthetic dataset is designed to mimic the conditions in California, where mc&#160;since 1970 is estimated to be around 3.5, and where a general decreasing trend in the temporal evolution of mc&#160;can be observed. Both models are trained on the primary catalog with identical time horizon. While the reference model is solely based on information about earthquakes of magnitude 3.5 and above, our alternative represents completeness magnitude as a monotonically decreasing step-function, starting at 3.5 and assuming values down to 2.1 in more recent times.To compare the two models, we issue forecasts by repeated probabilistic simulation of earthquake interaction scenarios, and evaluate those forecasts by assessing the likelihood of the actual occurrences under each of the alternatives. As a measure to quantify the difference in performance between the two models, we calculate the mean information gain due to model extension for different spatial resolutions, different temporal forecasting horizons, and different target magnitude ranges.Preliminary results suggest that the parameter bias introduced by successive application of simulation and inversion decreases exponentially with an increasing fraction of data used in the inversion. It is therefore expected that also the forecasting power of such a model increases with the amount of data available, indicating substantial importance of the method for the future of probabilistic seismic hazard assessment.

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Interaction of seismic background noise with oscillating pore fluids causes spectral modifications of passive seismic measurements at low frequencies

10.1190/1.2792742 ◽

2007 ◽

Cited By ~ 2

Author(s):

Marcel Frehner ◽

Stefan M. Schmalholz ◽

Yuri Podladchikov

Keyword(s):

Background Noise ◽

Pore Fluids ◽

Low Frequencies ◽

Passive Seismic ◽

Seismic Background ◽

Seismic Measurements

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Estimating the ETAS model from an early aftershock sequence

Geophysical Research Letters ◽

10.1002/2013gl058958 ◽

2014 ◽

Vol 41 (3) ◽

pp. 850-857 ◽

Cited By ~ 20

Author(s):

Takahiro Omi ◽

Yosihiko Ogata ◽

Yoshito Hirata ◽

Kazuyuki Aihara

Keyword(s):

Aftershock Sequence ◽

Etas Model

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Spatial Variations in Seismicity Characteristics in and Around the Source Region of the 2019 Yamagata-Oki Earthquake, Japan

10.21203/rs.3.rs-34752/v1 ◽

2020 ◽

Author(s):

Taku Ueda ◽

Aitaro Kato ◽

Yoshihiko Ogata ◽

Lina Yamaya

Keyword(s):

Source Region ◽

B Value ◽

Spatial Variations ◽

Japan Meteorological Agency ◽

Earthquake Catalog ◽

Shear Strain Rate ◽

Study Region ◽

Etas Model ◽

Seismicity Rate ◽

Background Seismicity

Abstract The 2019 {\text{M}}_{\text{j}} 6.7 Yamagata-Oki Earthquake occurred adjacent to the northeastern edge of the source region of the 1964 {\text{M}}_{\text{j}} 7.5 Niigata Earthquake, offshore of Yamagata Prefecture, Japan. Few aftershocks occurred in the source region of the Yamagata-Oki earthquake immediately following the Niigata earthquake, and the recent seismicity rate in this region is extremely low compared with that of the surrounding region. This spatial variation in seismicity may allow us to elucidate plausible physical processes that shape the spatiotemporal evolution of these shallow-crustal environments. Here, we investigate the spatial variations in seismicity characteristics by applying the HIerarchical Space–Time Epidemic Type Aftershock Sequence (HIST-ETAS) model to an earthquake catalog compiled by the Japan Meteorological Agency for events in and around the Yamagata-Oki earthquake rupture region. We compare spatial variations in the background seismicity rate and aftershock productivity estimated from the HIST-ETAS model with the geophysical features in the study region. The background seismicity rate is high along the eastern margin of the Sea of Japan and correlates well with a previously identified zone that possesses a high geodetic shear strain rate. The two major earthquakes occurred in and around an active shear zone, suggesting that the background seismicity rate may serve as a key parameter for evaluating seismic hazard across the Japanese Archipelago. Furthermore, the source region of the Yamagata-Oki earthquake has a higher aftershock productivity, lower b-value, and lower seismic-wave velocity than that of the Niigata earthquake. We interpret this low-velocity zone to be a well-developed damaged rock that resulted in both a reduction in the b-value and an increase in aftershock productivity based on previous laboratory experiments and numerical results; this damage makes the rock more ductile at the macroscopic scale. The higher ductility in the source region of the Yamagata-Oki earthquake may have worked as a soft barrier against the propagation of dynamic rupture that occurred during the Niigata earthquake.

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